Vol 17 No 7, July 2008 c© 2008 Chin. Phys. Soc.

1674-1056/2008/17(07)/2567-07 Chinese Physics B and IOP Publishing Ltd

A visible-near infrared tunable waveguidebased on plasmonic gold nanoshell∗

Zhang Hai-Xi(张海汐), Gu Ying(古 英)†, and Gong Qi-Huang(龚旗煌)‡

State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China

(Received 25 December 2007; revised manuscript received 29 January 2008)

A tunable plasmonic waveguide via gold nanoshells immerged in a silica base is proposed and simulated by using

the finite difference time-domain (FDTD) method. For waveguides based on near-field coupling, transmission frequencies

can be tuned in a wide region from 660 to 900 nm in wavelength by varying shell thicknesses. After exploring the steady

distributions of electric fields in these waveguides, we find that their decay lengths are about 5.948–12.83 dB/1000 nm,

which is superior to the decay length (8.947 dB/1000 nm) of a gold nanosphere plasmonic waveguide. These excellent

tunability and transmittability are mainly due to the unique hollow structure. These gold nanoshell waveguides should

be fabricated in laboratory.

Keywords: waveguide, surface plasmons, energy transferPACC: 4280L, 7320M

1. Introduction

Ordered arrays of closely spaced metallicnanoparticles are employed to transport optical sig-nals via near-field coupling.[1,2] Such structures, asplasmonic waveguides, allow the transport of elec-tromagnetic energy at optical frequencies below thediffraction limit. These structures also may be usedas the building blocks for the creation of nanoscale op-tical devices, optical circuits, and other near-field ap-plications. Quinten et al [3] analytically showed thatthe visible light could be transferred through a lin-ear chain of silver nanoparticles. A direct experi-mental demonstration of this plasmonic waveguide hasbeen pioneered by Maier et al.[4] Nanosphere waveg-uides have been widely studied qualitatively, for exam-ple, by treating the nanospheres as a coupled dipolechain.[5,6] Other plasmonic waveguides, formed by var-ious shaped nanoparticles, have been widely investi-gated as well.[7,8]

When the metallic nanoparticle waveguide is il-luminated on one tip and is surveyed on another tip,there exists a transmission (resonance) frequency de-fined by its best transmittability. This transmissionfrequency is different from the surface plasmon res-onance frequency of a single nanoparticle. The fre-

quency depends on the number of the nanoparticles,the spacing, and the specific structure in the waveg-uide. Too little a spacing leads to an insufficient near-field coupling between these particles and a more non-radiative loss as well. Nanosphere waveguide suffersfrom this limitation. With the radii of the nanosphereseach being 25 nm, their spacings each being 25 nm,and their immergence in a silica base, the transmis-sion wavelength of a nanosphere waveguide is almostuntunable at ∼555 nm. In this work, we employ thegold nanoshells as a block to design the tunable plas-monic waveguides. Many studies have substantiatedthat the gold nanoshell is a kind of versatile nanopho-tonic particle whose plasmon resonance can be tunedfrom a visible region to an infrared region by adjustingthe core/shell ratio.[9−11] Oldenburg et al [9] fabricatedgold nanoshells by way of molecular self-assemblyand colloidal growth chemistry. The gold nanoshell(< 100 nm) that is to be designed here has a silica corecoated with a thin gold shell. It can be fabricated bylayering a gold layer onto a silica nanoparticle.[12,13]

Recently, the smaller multi-layer gold nanoshells witha silica core have also been fabricated.[14]

The nanoshell waveguide in this work is composedof chain-like nanoshells each with an outer radius of25 nm and a spacing of 25 nm. By using an oscillat-

∗Project supported by the National Natural Science Foundation of China (Grants Nos 10674009, 10521002 and 10434020) and the

National Key Basic Research Program of China (Grant No 2007CB307001).†E-mail: ygu@pku.edu.cn‡E-mail: qhgong@pku.edu.cn

http://www.iop.org/journals/cpb　http://cpb.iphy.ac.cn

2568 Zhang Hai-Xi et al Vol. 17

ing point-dipole as the zeroth excited nanoshell, andperforming the Fourier transform to the time evo-lution of the electrical field from the FDTD simu-lation, we obtain the transmission frequency of thenanoshell waveguide. By changing the shell thickness,the transmission frequency is able to be tuned from avisible region to a near-infrared region, correspondingto the 660–900 nm wavelength range. For the 5 nm-thick nanoshell waveguide, the energy decay lengthof the steady distribution of the near-field is about5.948 dB/1000 nm due to the hollow structure, whichis superior to that of the nanosphere waveguide.[15]

Compared with the nanosphere waveguide, the 5 nm-thick nanoshell waveguide shows an effective tunabil-ity and an excellent transmittability. These plasmonicgold nanoshell waveguides should have potential appli-cations in nano-optics.

In the next section, we describe how we select theparameters of dielectric functions and how we set upthe FDTD simulation at the optical frequencies. InSection 3, the simulation results on the gold nanoshellplasmonic waveguides are shown and discussed in de-tail. Concluding remarks appear in Section 4.

2. Modification of the dielec-

tric function and the FDTD

method

As an effective numerical algorithm for the exactsolution to Maxwell’s equations, the finite-differencetime-domain (FDTD) method[16,17] and its ramifica-tion are a highly useful tool in studying the electro-magnetic responses for a heterogeneous material of ar-bitrary geometry.[18−21] Here we utilize the commer-cially available XFDTD 6.3.8.3 software (Remcom,Inc.). First, the experimental data of the bulk goldis modified to describe the size-dependent dielectricfunction of the metallic nanoshell at optical frequen-cies. To ensure the validity of our simulations, we setthe parameters such as mesh, stimulation dimensionand convergence degree elaborately. Then, accordingto these selected parameters, we obtain the surfaceplasmon resonance frequency for the specific nanos-tructure through the use of a pulse. The results forthe single nanoshells affirmed the accuracy of our sim-ulations. This approach should be applicable to find-ing out the transmission frequencies for the nanoshell

waveguides.The shell thickness here is only several nanome-

tres, much less than the gold electron mean-free path(∼42 nm). Dielectric function of a metallic nanopar-ticle will become size-dependent when the particle issmaller than the electron mean free path of the bulkmetal. The width of the absorption peak can be de-scribed as a modification of the bulk collisional fre-quency as shown below:[22]

Γ = γbulk + A× VF/a, (1)

where γbulk = VF/l0 is the bulk collisional frequency;VF is the Fermi speed; the gold electron mean freepath is l0 = 42 nm at room temperature; a is thereduced electron mean free path due to the surface;for the gold nanoshell, a is assumed to be equal to theshell thickness; A is the parameter which is dependenton the details of the surface scattering process.[23] Inthe context of the simple Drude theory and isotropicscattering, we chose A = 1. As a result, the size-dependent dielectric function of the gold nanoshells,ε(a, ω), becomes

ε(a, ω) = ε(ω)exp +ω2

p

ω2 + iωγbulk− ω2

p

ω2 + iωΓ, (2)

where ε(ω)exp is the experimental dielectricfunction,[24] and ωp = 6.274 × 1015 rad/s is the bulkplasmon frequency of gold. For the nanoshells in thenear-infrared and the visible regions, the dielectricfunction obtains an increase of the imaginary part,less than 50%; and a small increase in the real partfrom the modification. The half-width of the dipolarMie resonance peak of the single gold nanoshell is af-fected in the form of broadening and little redshift.[25]

In the XFDTD software, the dielectric function ε(ω)is described as

ε(ω) = ε∞ +εs − ε∞1 + iωτ

+σ

iωε0, (3)

where εs is the static permittivity at zero frequency,ε∞ is the infinite frequency permittivity, τ is the re-laxation time, and σ is the conductivity term.[16] Ina 600–1200 nm wavelength region, the modified datafrom expression (2) can be well fitted to expression (3).The parameters, obtained from the fitting to variousgold nanoshells, appear in Table 1. For the followingmodulated Gaussian pulse sources, these parameterscan be used directly.

No. 7 A visible-near infrared tunable waveguide based on plasmonic gold nanoshell 2569

Table 1. Parameters of gold nanoshells of different thicknesses.

thickness/nm (wavelength/nm) 3 (600–1200) 5 (600–1200) 7 (600–1000) bulk gold (650–1000)

σ 8.03185×106 9.83187×106 1.40456×107 1.48311×107

τ 5.06739×10−15 6.15573×10−15 8.76852×10−15 9.30635×10−15

εs –4.58501×103 –6.82362×103 –1.38881×104 –1.55794×104

ε∞ 8.27306 8.40669 8.48622 8.24384

For a specific nanostructure, we find out the sur-face plasmon resonance frequency in two steps. First,the object is illuminated with a modulated Gaussianpulse which contains many frequencies; then, we per-form the Fourier transform to the FDTD result, whichtraces the time evolution of the field for a certainpoint in the nanostructure, and take the weight ofeach frequency in the pulse into account. The fi-nal plots reveal the resonance frequency spectra fora certain point in the nanostructure. To verify the ac-curacy of this approach, we simulated the resonancefrequency of a single gold nanoshell. The simulationvolume consisted of a rectangular box of dimensions120 nm×120 nm×120 nm. The 50 nm outer-diametergold nanoshell, with a 40 nm diameter core (with a

dielectric constant of 5.44) was placed at the cen-tre of the volume. The particle was surrounded bya medium with a dielectric constant of 1.78. Thenanoshell was illuminated by a plane-wave propagat-ing in the z-direction with the electric field polarizedin the x-direction . The waveform of the plane wavewas chosen to be of the modulated Gaussian pulsewith a width of 0.8320 fs, and its frequency was set at4.28275×1014 Hz. The illumination covered the visibleregion and the near-infrared region. Figure 1(a) showsthe time evolution of the x-direction field at the cen-tre of the nanoshell. The Fourier transform plot dis-plays a single dipole peak centred at 3.97603×1014 Hz(≈ 754 nm) in Fig.1(b), which is in line with the result,about 750 nm determined by the Mie theory.[26]

Fig.1. (a) Time evolution of the electric field in the x-direction at the centre of single nanoshell and (b) Fourier

transform of Ex(t) with a dipole surface plasmon peak at 3.97603× 1014 Hz(∼754 nm).

Mesh size in all of our numerical simulations was1 nm, which provided both a good spatial resolutionand a low level of numerical spread error. We alsochecked the automatic convergence function (–35 dB),the Perfectly Matched Layers (8 layers), and the timestep of the XFDTD to make sure that our simula-tions gave a high accuracy and numerical stability inthe optical frequencies. To investigate the local er-ror that was introduced by the interaction between

the nanoshell and the PML boundary, we tested thesmaller computational domains (90×90×90 nm) withthe same mesh. In this case, the plasmon resonancefrequency was almost unchanged. For an array ofseven 50 nm gold nanospheres with a spacing of 75 nmin vacuum, we also checked the resonance peak at2.06 eV (about 602 nm).[27] The approach can be ef-fectively used for the nanoshell waveguides if the sim-ulation volume is correspondingly enlarged.

2570 Zhang Hai-Xi et al Vol. 17

3. Simulation results and discus-

sion

In our simulations, we have employed 15 or 25gold nanoshells each with an outer radius of 25 nmand a silica core to design the chain-like plasmonicwaveguides. The geometry of the nanoshell waveguideis depicted in Fig.2, where a 15–5 nm-thick nanoshellwaveguide is composed of 15 nanoshells each with athickness of 5 nm in shell. Unless otherwise stated,the centre-to-centre spacing is always 75 nm and thesurrounding medium is selected to be silica with arefractive index of 1.5067. To demonstrate the opti-cal signal propagation in a nanoshell waveguide, we

used a unit intensity oscillating point-dipole, whichwas placed at a distance of 75 nm from the centreof the first nanoshell, to represent an imaginary ex-cited zeroth nanoshell. The dipole, aligned parallel orperpendicular to the chain, corresponds to either thelongitudinal mode (LM) excitation or the transversemode (TM) excitation. As described in Section 2, tofind out the transmission frequency, which is definedby the strongest electric field appearing at the lastnanoshell, we used a modulated Gaussian pulse exci-tation, which covers the visual region and the near-infrared region, as a feed source. Taking the weight ofeach frequency in the modulated Gaussian pulse intoaccount, the Fourier transform plots reveal the trans-mission spectra for the waveguides.

Fig.2. The geometry of a 15–5 nm-thick nanoshell waveguide, with the outer radius of each nanoshell being 25 nm,

the centre-to-centre spacing being always 75 nm, and the core and the surrounding medium selected to be silica with

a refractive index of 1.5067.

The final LM and TM transmission spectra forthe 15–3 nm-thick, 15–5 nm-thick, and 15–7 nm-thickgold nanoshell waveguide are respectively shown inFigs.3(a) and 3(b). With the decrease in shellthickness, the transmission peaks become broadenedand red-shifted, which can be seen in the transmis-sion spectra. This broadening mainly comes fromthe inherent hollow structure and the many elec-tron collisions in the shell as compared with in a

nanosphere.[10,22,25] We have observed that the opticalsignals can be transported in certain frequency regionsdue to the existence of line-width in the transmis-sion spectra. Typically, for a 15–3 nm-thick nanoshellwaveguide, the transmission band covers a wide rangeof 600–900 nm in wavelength in its T mode. Figure3(c) shows that the tuned transmission frequencieswith the shell thickness varying in the 650–900 nmwavelength range. The nanoshell waveguides proved

Fig.3. Simulated optical transmission spectra of a nanoshell waveguide with the amplitude of the total field at the

centre of the last nanoshell versus the wavelength, for (a) L mode excitation and (b) T mode excitation. Panel (c) is

for the red shift plots of the transmission frequencies for the 15-nanoshell waveguides and 15-nanosphere waveguides,

where the upward triangle denotes the single nanoparticle of corresponding shell thickness.

No. 7 A visible-near infrared tunable waveguide based on plasmonic gold nanoshell 2571

to be superior to the nanosphere waveguides, whichcontain only a fixed transmission frequency (about555 nm in wavelength). In comparison with the sin-gle nanoshells, the nanoshell waveguide is shown tohave an approximate 10–20 nm red shift of the reso-nance position. For nanosphere waveguides, an ana-lytical approximate model as well as FDTD simula-tions (coarse scanning in frequency region) reckonedthe transmission frequencies just as the monomer res-onance frequencies.[15,28] Taking the cluster effect con-tribution into account, this 10–20 nm redshift is rea-sonable and accordant with the result which has beendemonstrated in nanosphere waveguide.[28,29] In oursimulations, the transmission wavelengths in T modeare always larger than the transmission wavelengths inL mode in Fig.3(c). Further simulations indicate that,with the same shell thicknesses, a 25-nanoshell waveg-uide almost possesses the same transmission frequencyas a 15-nanoshell waveguide. The above two resultsare reasonable and in line with the results obtainedfrom gold pad waveguides as well.[8] In conclusion, byvarying the nanoshell thickness, the transmission fre-

quency of the waveguide is effectively tuned from avisible region to a near-infrared region.

To account for the energy transmittability of theplasmonic waveguides, we explored the optical nearfield of the nanoshells as shown for T mode of 15–5 nm-thick nanoshell waveguide in Fig.4(a) and for L modeof 15–5 nm-thick nanoshell waveguide in Fig.4(b). Atthe transmission frequencies, the steady amplitudedistributions of the total field at the centre of eachshell are shown in Fig.5. If the input tip of the waveg-uide is illuminated in T mode, the electromagnetic en-ergy ceaselessly loses when it is transported along thewaveguide due to the radiative scattering and nonra-diative energy dissipation. When the energy is trans-ported into the terminal section of the waveguide,the near-field coupling is not so strong as that in theforepart, which partly gives place to the effect of a farfield superposition.[8] A steady transport emerges inits terminal section, in which the plot becomes an ap-proximately straight line as shown in Figs.5(a), 5(c),5(e) and 5(f).

Fig.4. Distributions of steady amplitudes of the total electric field at the median section for 15–5 nm-thick

nanoshell waveguides in their TM (a) and LM (b).

To estimate the energy transmissibility of Tmode, we fit straight lines to these curve tails. Thoughit is not very strict, this choice gives an excellent fitand it allows us to compare the decay lengths with theresults in the literature. The extracted energy decaylengths for the 25–3 nm-thick, and the 25–7 nm-thicknanoshell waveguides are 12.83 and 6.573 dB/1000 nm.Especially, the energy decay length for the trans-verse excitation of 25–5 nm-thick nanoshell waveguideis 5.948 dB/1000 nm, which is equal to about 730 nmin terms of the 1/e decay length. This energy de-cay is lower than 8.947/1000 nm of 25-nanospherewaveguide shown in Fig.5(f) and is obviously lowerthan those FDTD results obtained from a pulse-transporting simulation in the gold nanosphere waveg-uide (3 dB/140 nm for L mode; 3 dB/43 nm for T

mode).[15]

For the LM, the longitudinal strong near-fieldcoupling acts in the whole waveguide when the inputtip is illuminated. In the forepart of the waveguide,the rapid exponential decay is shown. The endpointeffect for the last few nanoshells is seen clearly in ourcalculation results.[5] Because for the LM, the trans-mission mainly benefits from the longitudinal strongnear-field coupling, this endpoint effect mainly comesfrom the longitudinal reflection of the last nanopar-ticle. Without the endpoint effect, a 15-nanoshellwaveguide shares an overlapping decay curve witha 25-nanoshell waveguide with the same shell thick-nesses. The L mode decay is undulating in its midst,like a stationary wave, which is subjected to the mul-tiple superposition and scattering of the strong near-

2572 Zhang Hai-Xi et al Vol. 17

field. Therefore its transmittability can be measuredby surveying the total field amplitude at the outputtip of the waveguide as shown in Figs.5(b), 5(d), 5(e)and 5(f). These plots show that the tunable nanoshellwaveguide is superior to the nanosphere waveguide inthe sense of the energy transmittability. Especially,surveying the total field amplitude at the centre of thelast nanoparticle, the 15–5 nm-thick nanoshell waveg-uide (LM) is superior to the 15–5 nm-thick nanospherewaveguide (LM) by three folds.

The above mentioned improvement on energytransmittability mainly arises from their unique hol-

low structure of the nanoshell waveguides. The in-trinsic tunability due to the hollow structure locatesthe transmission frequency in a certain optical rangewhere the dielectric losses are weaker. At the trans-mission frequency of the nanosphere waveguide (about555 nm in wavelength), the imaginary part of the di-electric constant for bulk gold is about 2.0. While,for the nanoshell waveguides with certain shell thick-nesses (≥5 nm), the modified imaginary parts of thedielectric constants at their transmission frequencies(660–900 nm in wavelength) are always less than 2.0.Furthermore, the hollow structure employs less metal-lic material, hence it reduces the nonradiative loss too.

Fig.5. Distributions of steady amplitudes of the total electric field at the centre of each nanoshell versus distance

in their transmission frequencies. Panels (a) and (b) are for the results for 15–5 nm-thick nanoshell waveguide and

25–5 nm-thick nanoshell waveguide (TM, LM). Panels (c) and (d) are for the results for 15–7 nm-thick nanoshell

waveguide and 25–7 nm-thick nanoshell waveguide (TM, LM). Panels (e) and (f) are for the results for 25–3 nm-thick

and 15–3 nm-thick nanoshell waveguides and 25- and 15- nanosphere waveguides.

4. Conclusions

We have presented a tunable plasmonic waveg-uide, based on the near-field coupling, and simulatedit by using the FDTD method. In order to ensure thevalidity of the FDTD method in simulation, we care-fully set and select various parameters. The transmis-sion frequencies are tuned in the visible region andthe near-infrared region (650–900 nm in wavelength)by utilizing different core/shell ratios. The transverse

mode of the nanoshell waveguide is found to have a lowlevel of energy decay as compared with the result ofthe gold nanosphere waveguide. For the longitudinalmode, a stronger near-field is observed in the outputtip than in the nanosphere waveguide. We attributethe improvement on tunability and transmittability tothe unique hollow structure of the nanoshell. Finally,we deem that this structure should be fabricated inlaboratory and it might be a good candidate for plas-monic devices.

No. 7 A visible-near infrared tunable waveguide based on plasmonic gold nanoshell 2573

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